Number is all, as the Pythagoreans recognized more than two millennia ago, but number is more obvious in some places than others. When you leaf through this book, you’re leafing through a catalogue of mathematical possibility: the endlessly varying shapes, sculptings, colours and patterns of seashells are in fact governed by evolutionary changes in a few relatively simple variables. The black-spotted, drill-like spiral of Terebra sublata might look very different from the orange-tinged, flattened, scorpion-like Lambis crocata, with its seven curved spikes, but the two species descend from the same ancestor as every other shell on display.

From the same ancestor as shell-less land- and sea-slugs too. But readers should remember that this book is a morgue as well as a museum: rich and beautiful as the shells are, the living animals and their biology are richer and more beautiful still. The living animals are sometimes deadly too: the very beautiful cone-shells have killed humans with their stings.

But the shell remains when the animal is dead, and can be collected and studied in isolation. That’s why almost all of the book is devoted to the more or less snail-like univalves, with the more or less scallop-like bivalves given only a few pages at the end. Generally speaking, univalve shells are much stronger and much more durable. They’re also more varied in both architecture and patterning: anyone who’s played with cascading cellular automata will often find the designs on the shells of cowries and cone-shells startlingly familiar. But they were doing it millions of years before us.

The cowries have a sexual charge too, with their tight, pudendal slits: their generic name, Cypraea, is taken from a title of Aphrodite, the Greek goddess of love. The apertures of other genera gape and glisten even more suggestively, imitating the labia of every human race and many abhuman ones. Is that part of the appeal of shell-collecting? I don’t know, but it doesn’t have to be, because it doesn’t appear in every shell and can’t be seen when the shells in which it does appear are turned over.

And they look better like that: Cypraea caputdraconis (sic), or the dragon’s-head cowrie, looks like unzipped black jeans lying on its back, but like a black, silver-flecked jewel lying on its front. It’s found only on Easter Island too, which is one of the many interesting snippets you can pick up from the short descriptions accompanying each highly skilled illustration.

But the illustrations aren’t, alas, as highly skilled as they could have been: in the reflections on many of them you can see the wooden dividers in the window of the room in which they were painted. That might have been quirkily attractive once or twice, but repeated over and over it becomes irritating. It could have been avoided, or the artist could have set up other reflections: palms, sea-birds, clouds, and even the moon or stars, as though the shells were still lying on a tropical beach.

Fortunately, it affects only the shiny and relatively undistorting surfaces of genera like the cowries and it’s only a minor blemish in a beautifully designed and well-written guide to a fascinating subject. And as always, the scientific names can have an appeal all of their own: we’ve already seen Cypraea caputdraconis, but what about Conus thalassiarchus, the Sea-Lord Cone, or Cirsotrema zelebori, whose meaning I have no idea of?